## Quintic surfaces of $$\mathbb{P}^ 3$$ having a non-singular model with $$q=p_ g=0$$, $$P_ 2\neq 0$$.(English)Zbl 0830.14013

Summary: In this paper we construct new examples of quintic surfaces of $$\mathbb{P}^3$$ having only isolated singularities $$(r$$ tacnodes or $$s$$ double points with infinitely near a tacnode, $$r + s = 4)$$ whose nonsingular model has irregularity $$q = 0$$ and invariants $$p_g = 0$$, $$P_2 \neq 0$$. In particular, an example is found of a quintic with a non singular model of general type.

### MSC:

 14J17 Singularities of surfaces or higher-dimensional varieties 14N05 Projective techniques in algebraic geometry

### Keywords:

quintic surfaces; isolated singularities
Full Text:

### References:

 [1] G. Castelnuovo , Sulle superficie di genere zero , Rend. Accad. Naz. Sci. dei XL , Mem. Mat., 10 ( 3 ) ( 1896 ), pp. 103 - 123 . JFM 27.0523.01 · JFM 27.0523.01 [2] F. Enriques - O. Chisini , Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche , Zanichelli , Bologna (ristampa 1985 ). Zbl 0009.15904 · Zbl 0009.15904 [3] Yonggu Kim , On Normal Quintic Enriques Surfaces , Ph.D. Thesis, University of Michigan ( 1991 ). · Zbl 0955.14026 [4] M. Reid , Campedelli, versus Godeaux, Symposia Mathematica Ist . Naz. Alta Matematica , Vol. XXXII ( 1989 ), pp. 309 - 365 . MR 1273384 [5] B. Segre , Prodromi di geometria algebrica , Cremonese , Roma ( 1972 ). Zbl 0281.14001 · Zbl 0281.14001 [6] E. Stagnaro , Constructing Enriques Surfaces from Quintics in Pk3, Algebraic Geometry. - Open Problems , Lectures Notes in Math., Springer Notes in Math . Springer-Verlag ( 1982 ), pp. 400 - 403 . MR 714760 | Zbl 0511.14020 · Zbl 0511.14020 [7] E. Stagnaro , Canonical and pluricanonical adjoints to an algebraic surfaces, I, R.T. n. 21 Ottobre 1991 ( Dip. di Metodi e Modelli Matematici per le Sc. Appl. dell’Università di Padova ). [8] Jin-Gen Yang , On quintic surfaces of general type , Trans. A.M.S. , 295 ( 2 ) ( 1986 ), pp. 431 - 472 . MR 833691 | Zbl 0596.14029 · Zbl 0596.14029
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